LMFDB - Embedded newform 300.2.x.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(17,300)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 13]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("300.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.x (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	300.17
Dual form			300.2.x.a.53.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73066 - 0.0694365i) q^{3} +(0.354250 + 2.20783i) q^{5} +(-1.67035 - 1.67035i) q^{7} +(2.99036 + 0.240342i) q^{9} +O(q^{10})$	\(q+(-1.73066 - 0.0694365i) q^{3} +(0.354250 + 2.20783i) q^{5} +(-1.67035 - 1.67035i) q^{7} +(2.99036 + 0.240342i) q^{9} +(-5.27981 + 1.71551i) q^{11} +(-1.00207 - 1.96667i) q^{13} +(-0.459783 - 3.84559i) q^{15} +(-4.25837 + 0.674459i) q^{17} +(-4.59013 + 6.31777i) q^{19} +(2.77483 + 3.00680i) q^{21} +(1.53667 - 3.01588i) q^{23} +(-4.74901 + 1.56425i) q^{25} +(-5.15860 - 0.623589i) q^{27} +(0.409155 - 0.297269i) q^{29} +(2.41697 + 1.75603i) q^{31} +(9.25666 - 2.60236i) q^{33} +(3.09613 - 4.27958i) q^{35} +(-7.68210 + 3.91423i) q^{37} +(1.59768 + 3.47321i) q^{39} +(4.48088 + 1.45593i) q^{41} +(5.88737 - 5.88737i) q^{43} +(0.528702 + 6.68734i) q^{45} +(-0.527820 + 3.33252i) q^{47} -1.41984i q^{49} +(7.41661 - 0.871573i) q^{51} +(5.21091 + 0.825328i) q^{53} +(-5.65793 - 11.0492i) q^{55} +(8.38263 - 10.6152i) q^{57} +(3.17139 - 9.76054i) q^{59} +(1.65928 + 5.10673i) q^{61} +(-4.59350 - 5.39641i) q^{63} +(3.98709 - 2.90909i) q^{65} +(0.707187 + 4.46500i) q^{67} +(-2.86886 + 5.11276i) q^{69} +(-6.04875 - 8.32540i) q^{71} +(-1.93067 - 0.983727i) q^{73} +(8.32754 - 2.37742i) q^{75} +(11.6847 + 5.95363i) q^{77} +(10.1110 + 13.9166i) q^{79} +(8.88447 + 1.43741i) q^{81} +(1.93251 + 12.2014i) q^{83} +(-2.99762 - 9.16282i) q^{85} +(-0.728750 + 0.486061i) q^{87} +(1.43321 + 4.41098i) q^{89} +(-1.61123 + 4.95884i) q^{91} +(-4.06102 - 3.20692i) q^{93} +(-15.5746 - 7.89614i) q^{95} +(-15.9942 - 2.53324i) q^{97} +(-16.2008 + 3.86104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q - 2 * q^3 + 4 * q^7	$ 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) $ 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.73066	−	0.0694365i	−0.999196	−	0.0400892i
$3$	−1.73066	−	0.0694365i	−0.999196	−	0.0400892i
$4$		0			0
$5$	0.354250	+	2.20783i	0.158426	+	0.987371i
$5$	0.354250	+	2.20783i	0.158426	+	0.987371i
$6$		0			0
$7$	−1.67035	−	1.67035i	−0.631334	−	0.631334i	0.317068	−	0.948403i	$-0.397302\pi$
$7$	−1.67035	−	1.67035i	−0.631334	−	0.631334i	−0.948403	+	0.317068i	$0.897302\pi$
$8$		0			0
$9$	2.99036	+	0.240342i	0.996786	+	0.0801139i
$10$		0			0
$11$	−5.27981	+	1.71551i	−1.59192	+	0.517247i	−0.965092	−	0.261910i	$-0.915648\pi$
$11$	−5.27981	+	1.71551i	−1.59192	+	0.517247i	−0.626830	+	0.779156i	$0.715648\pi$
$12$		0			0
$13$	−1.00207	−	1.96667i	−0.277924	−	0.545456i	0.709279	−	0.704928i	$-0.249021\pi$
$13$	−1.00207	−	1.96667i	−0.277924	−	0.545456i	−0.987202	+	0.159472i	$0.949021\pi$
$14$		0			0
$15$	−0.459783	−	3.84559i	−0.118715	−	0.992928i
$16$		0			0
$17$	−4.25837	+	0.674459i	−1.03281	+	0.163580i	−0.649753	−	0.760146i	$-0.725128\pi$
$17$	−4.25837	+	0.674459i	−1.03281	+	0.163580i	−0.383053	+	0.923726i	$0.625128\pi$
$18$		0			0
$19$	−4.59013	+	6.31777i	−1.05305	+	1.44940i	−0.166911	+	0.985972i	$0.553379\pi$
$19$	−4.59013	+	6.31777i	−1.05305	+	1.44940i	−0.886137	+	0.463423i	$0.846621\pi$
$20$		0			0
$21$	2.77483	+	3.00680i	0.605517	+	0.656136i
$22$		0			0
$23$	1.53667	−	3.01588i	0.320418	−	0.628855i	−0.673475	−	0.739210i	$-0.735199\pi$
$23$	1.53667	−	3.01588i	0.320418	−	0.628855i	0.993892	+	0.110355i	$0.0351989\pi$
$24$		0			0
$25$	−4.74901	+	1.56425i	−0.949803	+	0.312850i
$26$		0			0
$27$	−5.15860	−	0.623589i	−0.992773	−	0.120010i
$28$		0			0
$29$	0.409155	−	0.297269i	0.0759783	−	0.0552014i	−0.549148	−	0.835725i	$-0.685048\pi$
$29$	0.409155	−	0.297269i	0.0759783	−	0.0552014i	0.625126	+	0.780524i	$0.285048\pi$
$30$		0			0
$31$	2.41697	+	1.75603i	0.434101	+	0.315393i	0.783287	−	0.621661i	$-0.213542\pi$
$31$	2.41697	+	1.75603i	0.434101	+	0.315393i	−0.349186	+	0.937054i	$0.613542\pi$
$32$		0			0
$33$	9.25666	−	2.60236i	1.61138	−	0.453012i
$34$		0			0
$35$	3.09613	−	4.27958i	0.523342	−	0.723381i
$36$		0			0
$37$	−7.68210	+	3.91423i	−1.26293	+	0.643495i	−0.951755	−	0.306858i	$-0.900722\pi$
$37$	−7.68210	+	3.91423i	−1.26293	+	0.643495i	−0.311174	+	0.950353i	$0.600722\pi$
$38$		0			0
$39$	1.59768	+	3.47321i	0.255833	+	0.556159i
$40$		0			0
$41$	4.48088	+	1.45593i	0.699796	+	0.227377i	0.637242	−	0.770664i	$-0.280075\pi$
$41$	4.48088	+	1.45593i	0.699796	+	0.227377i	0.0625543	+	0.998042i	$0.480075\pi$
$42$		0			0
$43$	5.88737	−	5.88737i	0.897816	−	0.897816i	−0.0974269	−	0.995243i	$-0.531061\pi$
$43$	5.88737	−	5.88737i	0.897816	−	0.897816i	0.995243	+	0.0974269i	$0.0310612\pi$
$44$		0			0
$45$	0.528702	+	6.68734i	0.0788143	+	0.996889i
$46$		0			0
$47$	−0.527820	+	3.33252i	−0.0769905	+	0.486099i	0.918821	+	0.394673i	$0.129142\pi$
$47$	−0.527820	+	3.33252i	−0.0769905	+	0.486099i	−0.995812	+	0.0914252i	$0.970858\pi$
$48$		0			0
$49$		−	1.41984i		−	0.202834i
$50$		0			0
$51$	7.41661	−	0.871573i	1.03853	−	0.122045i
$52$		0			0
$53$	5.21091	+	0.825328i	0.715774	+	0.113367i	0.503691	−	0.863884i	$-0.331975\pi$
$53$	5.21091	+	0.825328i	0.715774	+	0.113367i	0.212083	+	0.977252i	$0.431975\pi$
$54$		0			0
$55$	−5.65793	−	11.0492i	−0.762916	−	1.48987i
$56$		0			0
$57$	8.38263	−	10.6152i	1.11031	−	1.40601i
$58$		0			0
$59$	3.17139	−	9.76054i	0.412880	−	1.27071i	−0.501254	−	0.865300i	$-0.667128\pi$
$59$	3.17139	−	9.76054i	0.412880	−	1.27071i	0.914134	−	0.405413i	$-0.132872\pi$
$60$		0			0
$61$	1.65928	+	5.10673i	0.212449	+	0.653850i	0.999325	+	0.0367391i	$0.0116970\pi$
$61$	1.65928	+	5.10673i	0.212449	+	0.653850i	−0.786876	+	0.617111i	$0.788303\pi$
$62$		0			0
$63$	−4.59350	−	5.39641i	−0.578726	−	0.679884i
$64$		0			0
$65$	3.98709	−	2.90909i	0.494537	−	0.360828i
$66$		0			0
$67$	0.707187	+	4.46500i	0.0863966	+	0.545487i	0.992482	+	0.122392i	$0.0390564\pi$
$67$	0.707187	+	4.46500i	0.0863966	+	0.545487i	−0.906085	+	0.423095i	$0.860944\pi$
$68$		0			0
$69$	−2.86886	+	5.11276i	−0.345370	+	0.615504i
$70$		0			0
$71$	−6.04875	−	8.32540i	−0.717855	−	0.988043i	−0.999592	−	0.0285511i	$-0.990911\pi$
$71$	−6.04875	−	8.32540i	−0.717855	−	0.988043i	0.281737	−	0.959492i	$-0.409089\pi$
$72$		0			0
$73$	−1.93067	−	0.983727i	−0.225968	−	0.115136i	0.337342	−	0.941382i	$-0.390472\pi$
$73$	−1.93067	−	0.983727i	−0.225968	−	0.115136i	−0.563310	+	0.826246i	$0.690472\pi$
$74$		0			0
$75$	8.32754	−	2.37742i	0.961581	−	0.274521i
$76$		0			0
$77$	11.6847	+	5.95363i	1.33159	+	0.678479i
$78$		0			0
$79$	10.1110	+	13.9166i	1.13757	+	1.56574i	0.772811	+	0.634637i	$0.218850\pi$
$79$	10.1110	+	13.9166i	1.13757	+	1.56574i	0.364764	+	0.931100i	$0.381150\pi$
$80$		0			0
$81$	8.88447	+	1.43741i	0.987164	+	0.159713i
$82$		0			0
$83$	1.93251	+	12.2014i	0.212121	+	1.33928i	0.832085	+	0.554648i	$0.187147\pi$
$83$	1.93251	+	12.2014i	0.212121	+	1.33928i	−0.619964	+	0.784630i	$0.712853\pi$
$84$		0			0
$85$	−2.99762	−	9.16282i	−0.325137	−	0.993847i
$86$		0			0
$87$	−0.728750	+	0.486061i	−0.0781302	+	0.0521112i
$88$		0			0
$89$	1.43321	+	4.41098i	0.151920	+	0.467563i	0.997836	−	0.0657541i	$-0.0209453\pi$
$89$	1.43321	+	4.41098i	0.151920	+	0.467563i	−0.845915	+	0.533317i	$0.820945\pi$
$90$		0			0
$91$	−1.61123	+	4.95884i	−0.168902	+	0.519828i
$92$		0			0
$93$	−4.06102	−	3.20692i	−0.421108	−	0.332542i
$94$		0			0
$95$	−15.5746	−	7.89614i	−1.59792	−	0.810127i
$96$		0			0
$97$	−15.9942	−	2.53324i	−1.62397	−	0.257211i	−0.722921	−	0.690931i	$-0.757201\pi$
$97$	−15.9942	−	2.53324i	−1.62397	−	0.257211i	−0.901048	+	0.433720i	$0.857201\pi$
$98$		0			0
$99$	−16.2008	+	3.86104i	−1.62824	+	0.388049i
$100$		0			0
$101$			4.67239i			0.464920i	0.972606	+	0.232460i	$0.0746775\pi$
$101$			4.67239i			0.464920i	−0.972606	+	0.232460i	$0.925322\pi$
$102$		0			0
$103$	−1.07022	+	6.75713i	−0.105452	+	0.665800i	0.877169	+	0.480181i	$0.159429\pi$
$103$	−1.07022	+	6.75713i	−0.105452	+	0.665800i	−0.982622	+	0.185619i	$0.940571\pi$
$104$		0			0
$105$	−5.65550	+	7.19150i	−0.551921	+	0.701819i
$106$		0			0
$107$	−2.84075	+	2.84075i	−0.274626	+	0.274626i	−0.830959	−	0.556334i	$-0.812208\pi$
$107$	−2.84075	+	2.84075i	−0.274626	+	0.274626i	0.556334	+	0.830959i	$0.312208\pi$
$108$		0			0
$109$	−10.7758	−	3.50126i	−1.03213	−	0.335360i	−0.256499	−	0.966544i	$-0.582569\pi$
$109$	−10.7758	−	3.50126i	−1.03213	−	0.335360i	−0.775633	+	0.631185i	$0.782569\pi$
$110$		0			0
$111$	13.5669	−	6.24077i	1.28771	−	0.592348i
$112$		0			0
$113$	3.85613	−	1.96480i	0.362754	−	0.184833i	−0.263108	−	0.964767i	$-0.584747\pi$
$113$	3.85613	−	1.96480i	0.362754	−	0.184833i	0.625862	+	0.779934i	$0.284747\pi$
$114$		0			0
$115$	7.20292	+	2.32432i	0.671675	+	0.216744i
$116$		0			0
$117$	−2.52387	−	6.12188i	−0.233332	−	0.565968i
$118$		0			0
$119$	8.23957	+	5.98640i	0.755320	+	0.548772i
$120$		0			0
$121$	16.0342	−	11.6495i	1.45765	−	1.05905i
$122$		0			0
$123$	−7.65378	−	2.83085i	−0.690118	−	0.255249i
$124$		0			0
$125$	−5.13593	−	9.93087i	−0.459372	−	0.888244i
$126$		0			0
$127$	−0.759425	+	1.49046i	−0.0673881	+	0.132257i	−0.922243	−	0.386610i	$-0.873646\pi$
$127$	−0.759425	+	1.49046i	−0.0673881	+	0.132257i	0.854855	+	0.518867i	$0.173646\pi$
$128$		0			0
$129$	−10.5978	+	9.78023i	−0.933087	+	0.861101i
$130$		0			0
$131$	−2.70065	+	3.71712i	−0.235957	+	0.324767i	−0.910531	−	0.413440i	$-0.864327\pi$
$131$	−2.70065	+	3.71712i	−0.235957	+	0.324767i	0.674575	+	0.738207i	$0.264327\pi$
$132$		0			0
$133$	18.2200	−	2.88577i	1.57988	−	0.250228i
$134$		0			0
$135$	−0.450658	−	11.6102i	−0.0387865	−	0.999248i
$136$		0			0
$137$	−4.03906	−	7.92710i	−0.345080	−	0.677258i	0.651610	−	0.758554i	$-0.274094\pi$
$137$	−4.03906	−	7.92710i	−0.345080	−	0.677258i	−0.996690	+	0.0812966i	$0.974094\pi$
$138$		0			0
$139$	3.53260	−	1.14781i	0.299631	−	0.0973561i	−0.155343	−	0.987861i	$-0.549648\pi$
$139$	3.53260	−	1.14781i	0.299631	−	0.0973561i	0.454975	+	0.890504i	$0.349648\pi$
$140$		0			0
$141$	1.14487	−	5.73081i	0.0964158	−	0.482621i
$142$		0			0
$143$	8.66458	+	8.66458i	0.724568	+	0.724568i
$144$		0			0
$145$	0.801262	+	0.798037i	0.0665412	+	0.0662734i
$146$		0			0
$147$	−0.0985885	+	2.45725i	−0.00813144	+	0.202671i
$148$		0			0
$149$	−16.5291			−1.35411			−0.677057	−	0.735931i	$-0.736745\pi$
$149$	−16.5291			−1.35411			−0.677057	+	0.735931i	$0.736745\pi$
$150$		0			0
$151$	−5.27383			−0.429178			−0.214589	−	0.976704i	$-0.568841\pi$
$151$	−5.27383			−0.429178			−0.214589	+	0.976704i	$0.568841\pi$
$152$		0			0
$153$	−12.8961	+	0.993411i	−1.04259	+	0.0803125i
$154$		0			0
$155$	−3.02081	+	5.95833i	−0.242637	+	0.478585i
$156$		0			0
$157$	7.79069	+	7.79069i	0.621765	+	0.621765i	0.945982	−	0.324218i	$-0.105101\pi$
$157$	7.79069	+	7.79069i	0.621765	+	0.621765i	−0.324218	+	0.945982i	$0.605101\pi$
$158$		0			0
$159$	−8.96100	−	1.79019i	−0.710654	−	0.141971i
$160$		0			0
$161$	−7.60437	+	2.47081i	−0.599308	+	0.194727i
$162$		0			0
$163$	−7.02791	−	13.7931i	−0.550469	−	1.08036i	−0.983825	−	0.179133i	$-0.942671\pi$
$163$	−7.02791	−	13.7931i	−0.550469	−	1.08036i	0.433356	−	0.901223i	$-0.357329\pi$
$164$		0			0
$165$	9.02473	+	19.5152i	0.702575	+	1.51926i
$166$		0			0
$167$	−9.92370	+	1.57176i	−0.767919	+	0.121626i	−0.528090	−	0.849189i	$-0.677092\pi$
$167$	−9.92370	+	1.57176i	−0.767919	+	0.121626i	−0.239829	+	0.970815i	$0.577092\pi$
$168$		0			0
$169$	4.77756	−	6.57575i	0.367505	−	0.505827i
$170$		0			0
$171$	−15.2445	+	17.7892i	−1.16578	+	1.36037i
$172$		0			0
$173$	−6.65343	+	13.0581i	−0.505851	+	0.992789i	0.486997	+	0.873404i	$0.338092\pi$
$173$	−6.65343	+	13.0581i	−0.505851	+	0.992789i	−0.992848	+	0.119385i	$0.961908\pi$
$174$		0			0
$175$	10.5454	+	5.31968i	0.797156	+	0.402130i
$176$		0			0
$177$	−6.16633	+	16.6719i	−0.463490	+	1.25314i
$178$		0			0
$179$	12.3066	−	8.94125i	0.919837	−	0.668301i	−0.0236465	−	0.999720i	$-0.507528\pi$
$179$	12.3066	−	8.94125i	0.919837	−	0.668301i	0.943483	+	0.331420i	$0.107528\pi$
$180$		0			0
$181$	0.447095	+	0.324833i	0.0332323	+	0.0241447i	0.604277	−	0.796774i	$-0.293462\pi$
$181$	0.447095	+	0.324833i	0.0332323	+	0.0241447i	−0.571045	+	0.820919i	$0.693462\pi$
$182$		0			0
$183$	−2.51705	−	8.95322i	−0.186066	−	0.661841i
$184$		0			0
$185$	−11.3633	−	15.5741i	−0.835448	−	1.14503i
$186$		0			0
$187$	21.3263	−	10.8663i	1.55954	−	0.794623i
$188$		0			0
$189$	7.57507	+	9.65830i	0.551005	+	0.702538i
$190$		0			0
$191$	−20.5690	−	6.68327i	−1.48832	−	0.483585i	−0.551734	−	0.834020i	$-0.686034\pi$
$191$	−20.5690	−	6.68327i	−1.48832	−	0.483585i	−0.936587	+	0.350435i	$0.886034\pi$
$192$		0			0
$193$	−3.71609	+	3.71609i	−0.267490	+	0.267490i	−0.828088	−	0.560598i	$-0.810571\pi$
$193$	−3.71609	+	3.71609i	−0.267490	+	0.267490i	0.560598	+	0.828088i	$0.310571\pi$
$194$		0			0
$195$	−7.10228	+	4.75779i	−0.508605	+	0.340712i
$196$		0			0
$197$	−3.06376	+	19.3438i	−0.218284	+	1.37819i	0.598442	+	0.801166i	$0.295787\pi$
$197$	−3.06376	+	19.3438i	−0.218284	+	1.37819i	−0.816726	+	0.577026i	$0.804213\pi$
$198$		0			0
$199$		−	1.77115i		−	0.125553i	−0.998028	−	0.0627766i	$-0.980004\pi$
$199$		−	1.77115i		−	0.125553i	0.998028	−	0.0627766i	$-0.0199956\pi$
$200$		0			0
$201$	−0.913865	−	7.77649i	−0.0644590	−	0.548512i
$202$		0			0
$203$	−1.17998	−	0.186890i	−0.0828182	−	0.0131171i
$204$		0			0
$205$	−1.62708	+	10.4088i	−0.113640	+	0.726980i
$206$		0			0
$207$	5.32003	−	8.64924i	0.369768	−	0.601164i
$208$		0			0
$209$	13.3968	−	41.2310i	0.926674	−	2.85201i
$210$		0			0
$211$	0.990096	+	3.04720i	0.0681610	+	0.209778i	0.979335	−	0.202243i	$-0.0648230\pi$
$211$	0.990096	+	3.04720i	0.0681610	+	0.209778i	−0.911174	+	0.412021i	$0.864823\pi$
$212$		0			0
$213$	9.89024	+	14.8284i	0.677668	+	1.01603i
$214$		0			0
$215$	15.0839	+	10.9127i	1.02871	+	0.744240i
$216$		0			0
$217$	−1.10400	−	6.97039i	−0.0749445	−	0.473181i
$218$		0			0
$219$	3.27303	+	1.83655i	0.221171	+	0.124103i
$220$		0			0
$221$	5.59361	+	7.69895i	0.376267	+	0.517887i
$222$		0			0
$223$	−2.15039	−	1.09568i	−0.144001	−	0.0733720i	0.380505	−	0.924779i	$-0.375750\pi$
$223$	−2.15039	−	1.09568i	−0.144001	−	0.0733720i	−0.524506	+	0.851407i	$0.675750\pi$
$224$		0			0
$225$	−14.5772	+	3.53628i	−0.971813	+	0.235752i
$226$		0			0
$227$	14.3886	+	7.33136i	0.955005	+	0.486599i	0.860794	−	0.508953i	$-0.169967\pi$
$227$	14.3886	+	7.33136i	0.955005	+	0.486599i	0.0942105	+	0.995552i	$0.469967\pi$
$228$		0			0
$229$	−10.1726	−	14.0013i	−0.672222	−	0.925235i	0.327586	−	0.944821i	$-0.393765\pi$
$229$	−10.1726	−	14.0013i	−0.672222	−	0.925235i	−0.999808	+	0.0195869i	$0.993765\pi$
$230$		0			0
$231$	−19.8088	−	11.1150i	−1.30332	−	0.731316i
$232$		0			0
$233$	−2.40288	−	15.1712i	−0.157418	−	0.993898i	−0.932272	−	0.361758i	$-0.882177\pi$
$233$	−2.40288	−	15.1712i	−0.157418	−	0.993898i	0.774854	−	0.632140i	$-0.217823\pi$
$234$		0			0
$235$	−7.54462	+	0.0152120i	−0.492157	+	0.000992319i
$236$		0			0
$237$	−16.5323	−	24.7869i	−1.07389	−	1.61008i
$238$		0			0
$239$	6.17815	+	19.0144i	0.399631	+	1.22994i	0.925296	+	0.379247i	$0.123817\pi$
$239$	6.17815	+	19.0144i	0.399631	+	1.22994i	−0.525664	+	0.850692i	$0.676183\pi$
$240$		0			0
$241$	1.32659	−	4.08282i	0.0854532	−	0.262998i	−0.899195	−	0.437548i	$-0.855847\pi$
$241$	1.32659	−	4.08282i	0.0854532	−	0.262998i	0.984648	+	0.174550i	$0.0558471\pi$
$242$		0			0
$243$	−15.2762	−	3.10458i	−0.979967	−	0.199159i
$244$		0			0
$245$	3.13476	−	0.502978i	0.200272	−	0.0321341i
$246$		0			0
$247$	17.0246	+	2.69643i	1.08325	+	0.171570i
$248$		0			0
$249$	−2.49730	−	21.2506i	−0.158260	−	1.34671i
$250$		0			0
$251$			7.64733i			0.482695i	0.970439	+	0.241347i	$0.0775893\pi$
$251$			7.64733i			0.482695i	−0.970439	+	0.241347i	$0.922411\pi$
$252$		0			0
$253$	−2.93953	+	18.5595i	−0.184807	+	1.16682i
$254$		0			0
$255$	4.55162	+	16.0659i	0.285034	+	1.00608i
$256$		0			0
$257$	−6.23777	+	6.23777i	−0.389101	+	0.389101i	−0.874367	−	0.485266i	$-0.838723\pi$
$257$	−6.23777	+	6.23777i	−0.389101	+	0.389101i	0.485266	+	0.874367i	$0.338723\pi$
$258$		0			0
$259$	19.3700	+	6.29368i	1.20359	+	0.391070i
$260$		0			0
$261$	1.29497	−	0.790603i	0.0801564	−	0.0489371i
$262$		0			0
$263$	15.4727	−	7.88374i	0.954088	−	0.486132i	0.0936037	−	0.995610i	$-0.470161\pi$
$263$	15.4727	−	7.88374i	0.954088	−	0.486132i	0.860484	+	0.509478i	$0.170161\pi$
$264$		0			0
$265$	0.0237862	+	11.7972i	0.00146118	+	0.724695i
$266$		0			0
$267$	−2.17412	−	7.73342i	−0.133054	−	0.473277i
$268$		0			0
$269$	17.2020	+	12.4980i	1.04883	+	0.762017i	0.971989	−	0.235026i	$-0.0755176\pi$
$269$	17.2020	+	12.4980i	1.04883	+	0.762017i	0.0768379	+	0.997044i	$0.475518\pi$
$270$		0			0
$271$	−7.79739	+	5.66514i	−0.473658	+	0.344133i	−0.798865	−	0.601510i	$-0.794566\pi$
$271$	−7.79739	+	5.66514i	−0.473658	+	0.344133i	0.325207	+	0.945643i	$0.394566\pi$
$272$		0			0
$273$	3.13280	−	8.47018i	0.189606	−	0.512639i
$274$		0			0
$275$	22.3904	−	16.4059i	1.35019	−	0.989315i
$276$		0			0
$277$	14.6228	−	28.6988i	0.878596	−	1.72434i	0.214455	−	0.976734i	$-0.431202\pi$
$277$	14.6228	−	28.6988i	0.878596	−	1.72434i	0.664141	−	0.747608i	$-0.268798\pi$
$278$		0			0
$279$	6.80556	+	5.83206i	0.407438	+	0.349157i
$280$		0			0
$281$	−1.62290	+	2.23373i	−0.0968141	+	0.133253i	−0.854676	−	0.519162i	$-0.826244\pi$
$281$	−1.62290	+	2.23373i	−0.0968141	+	0.133253i	0.757862	+	0.652415i	$0.226244\pi$
$282$		0			0
$283$	−15.0519	+	2.38398i	−0.894741	+	0.141713i	−0.586838	−	0.809705i	$-0.699627\pi$
$283$	−15.0519	+	2.38398i	−0.894741	+	0.141713i	−0.307903	+	0.951418i	$0.599627\pi$
$284$		0			0
$285$	26.4060	+	14.7470i	1.56416	+	0.873535i
$286$		0			0
$287$	−5.05274	−	9.91657i	−0.298254	−	0.585356i
$288$		0			0
$289$	1.51085	−	0.490904i	0.0888733	−	0.0288767i
$290$		0			0
$291$	27.5047	+	5.49475i	1.61235	+	0.322108i
$292$		0			0
$293$	7.47364	+	7.47364i	0.436615	+	0.436615i	0.890871	−	0.454256i	$-0.150095\pi$
$293$	7.47364	+	7.47364i	0.436615	+	0.436615i	−0.454256	+	0.890871i	$0.650095\pi$
$294$		0			0
$295$	22.6731	+	3.54421i	1.32008	+	0.206352i
$296$		0			0
$297$	28.3062	−	5.55722i	1.64249	−	0.322462i
$298$		0			0
$299$	−7.47109			−0.432064
$300$		0			0
$301$	−19.6680			−1.13364
$302$		0			0
$303$	0.324434	−	8.08631i	0.0186383	−	0.464547i
$304$		0			0
$305$	−10.6870	+	5.47246i	−0.611935	+	0.313352i
$306$		0			0
$307$	3.64430	+	3.64430i	0.207991	+	0.207991i	0.803413	−	0.595422i	$-0.203015\pi$
$307$	3.64430	+	3.64430i	0.207991	+	0.207991i	−0.595422	+	0.803413i	$0.703015\pi$
$308$		0			0
$309$	2.32139	−	11.6200i	0.132059	−	0.661038i
$310$		0			0
$311$	7.97750	−	2.59205i	0.452363	−	0.146982i	−0.0739696	−	0.997260i	$-0.523567\pi$
$311$	7.97750	−	2.59205i	0.452363	−	0.146982i	0.526332	+	0.850279i	$0.323567\pi$
$312$		0			0
$313$	4.02979	+	7.90891i	0.227777	+	0.447038i	0.976403	−	0.215954i	$-0.0692863\pi$
$313$	4.02979	+	7.90891i	0.227777	+	0.447038i	−0.748626	+	0.662992i	$0.769286\pi$
$314$		0			0
$315$	10.2871	−	12.0533i	0.579612	−	0.679129i
$316$		0			0
$317$	−14.6748	+	2.32426i	−0.824218	+	0.130543i	−0.554276	−	0.832333i	$-0.687005\pi$
$317$	−14.6748	+	2.32426i	−0.824218	+	0.130543i	−0.269943	+	0.962876i	$0.587005\pi$
$318$		0			0
$319$	−1.65029	+	2.27143i	−0.0923987	+	0.127176i
$320$		0			0
$321$	5.11362	−	4.71911i	0.285414	−	0.263395i
$322$		0			0
$323$	15.2854	−	29.9992i	0.850501	−	1.66920i
$324$		0			0
$325$	7.83519	+	7.77226i	0.434618	+	0.431127i
$326$		0			0
$327$	18.4061	+	6.80772i	1.01786	+	0.376468i
$328$		0			0
$329$	6.44814	−	4.68485i	0.355497	−	0.258284i
$330$		0			0
$331$	−9.59179	−	6.96885i	−0.527213	−	0.383042i	0.292101	−	0.956387i	$-0.405646\pi$
$331$	−9.59179	−	6.96885i	−0.527213	−	0.383042i	−0.819314	+	0.573345i	$0.805646\pi$
$332$		0			0
$333$	−23.9130	+	9.85860i	−1.31042	+	0.540248i
$334$		0			0
$335$	−9.60743	+	3.14307i	−0.524910	+	0.171725i
$336$		0			0
$337$	−9.98022	+	5.08518i	−0.543657	+	0.277007i	−0.704176	−	0.710026i	$-0.748683\pi$
$337$	−9.98022	+	5.08518i	−0.543657	+	0.277007i	0.160519	+	0.987033i	$0.448683\pi$
$338$		0			0
$339$	−6.81007	+	3.13264i	−0.369872	+	0.170141i
$340$		0			0
$341$	−15.7736	−	5.12517i	−0.854191	−	0.277543i
$342$		0			0
$343$	−14.0641	+	14.0641i	−0.759390	+	0.759390i
$344$		0			0
$345$	−12.3044	−	4.52276i	−0.662446	−	0.243497i
$346$		0			0
$347$	−4.46050	+	28.1625i	−0.239452	+	1.51184i	0.515972	+	0.856606i	$0.327431\pi$
$347$	−4.46050	+	28.1625i	−0.239452	+	1.51184i	−0.755424	+	0.655236i	$0.772569\pi$
$348$		0			0
$349$		−	24.5531i		−	1.31430i	−0.753761	−	0.657149i	$-0.771762\pi$
$349$		−	24.5531i		−	1.31430i	0.753761	−	0.657149i	$-0.228238\pi$
$350$		0			0
$351$	3.94287	+	10.7701i	0.210455	+	0.574867i
$352$		0			0
$353$	7.23776	+	1.14635i	0.385227	+	0.0610140i	0.346045	−	0.938218i	$-0.387525\pi$
$353$	7.23776	+	1.14635i	0.385227	+	0.0610140i	0.0391827	+	0.999232i	$0.487525\pi$
$354$		0			0
$355$	16.2383	−	16.3039i	0.861838	−	0.865320i
$356$		0			0
$357$	−13.8442	−	10.9325i	−0.732713	−	0.578611i
$358$		0			0
$359$	3.41890	−	10.5223i	0.180443	−	0.555345i	−0.819397	−	0.573226i	$-0.805692\pi$
$359$	3.41890	−	10.5223i	0.180443	−	0.555345i	0.999840	+	0.0178804i	$0.00569180\pi$
$360$		0			0
$361$	−12.9736	−	39.9287i	−0.682821	−	2.10151i
$362$		0			0
$363$	−28.5586	+	19.0480i	−1.49894	+	0.999760i
$364$		0			0
$365$	1.48796	−	4.61108i	0.0778833	−	0.241355i
$366$		0			0
$367$	5.39806	+	34.0820i	0.281776	+	1.77907i	0.570142	+	0.821546i	$0.306888\pi$
$367$	5.39806	+	34.0820i	0.281776	+	1.77907i	−0.288366	+	0.957520i	$0.593112\pi$
$368$		0			0
$369$	13.0495	+	5.43068i	0.679330	+	0.282710i
$370$		0			0
$371$	−7.32548	−	10.0827i	−0.380320	−	0.523465i
$372$		0			0
$373$	14.7942	+	7.53802i	0.766014	+	0.390304i	0.792913	−	0.609335i	$-0.208563\pi$
$373$	14.7942	+	7.53802i	0.766014	+	0.390304i	−0.0268992	+	0.999638i	$0.508563\pi$
$374$		0			0
$375$	8.19898	+	17.5436i	0.423393	+	0.905946i
$376$		0			0
$377$	−0.994631	−	0.506790i	−0.0512261	−	0.0261010i
$378$		0			0
$379$	−20.3628	−	28.0270i	−1.04597	−	1.43965i	−0.892255	−	0.451532i	$-0.850878\pi$
$379$	−20.3628	−	28.0270i	−1.04597	−	1.43965i	−0.153711	−	0.988116i	$-0.549122\pi$
$380$		0			0
$381$	1.41780	−	2.52674i	0.0726359	−	0.129449i
$382$		0			0
$383$	3.45899	+	21.8392i	0.176746	+	1.11593i	0.903359	+	0.428885i	$0.141094\pi$
$383$	3.45899	+	21.8392i	0.176746	+	1.11593i	−0.726613	+	0.687047i	$0.758906\pi$
$384$		0			0
$385$	−9.00530	+	27.9068i	−0.458953	+	1.42226i
$386$		0			0
$387$	19.0203	−	16.1904i	0.966857	−	0.823003i
$388$		0			0
$389$	0.876383	+	2.69723i	0.0444344	+	0.136755i	0.970812	−	0.239840i	$-0.0770949\pi$
$389$	0.876383	+	2.69723i	0.0444344	+	0.136755i	−0.926378	+	0.376595i	$0.877095\pi$
$390$		0			0
$391$	−4.50961	+	13.8792i	−0.228061	+	0.701899i
$392$		0			0
$393$	4.93200	−	6.24555i	0.248787	−	0.315046i
$394$		0			0
$395$	−27.1436	+	27.2533i	−1.36574	+	1.37126i
$396$		0			0
$397$	−29.9879	−	4.74962i	−1.50505	−	0.238377i	−0.651205	−	0.758902i	$-0.725736\pi$
$397$	−29.9879	−	4.74962i	−1.50505	−	0.238377i	−0.853846	+	0.520525i	$0.825736\pi$
$398$		0			0
$399$	−31.7331	+	3.72915i	−1.58864	+	0.186691i
$400$		0			0
$401$		−	33.3974i		−	1.66779i	−0.551925	−	0.833894i	$-0.686107\pi$
$401$		−	33.3974i		−	1.66779i	0.551925	−	0.833894i	$-0.313893\pi$
$402$		0			0
$403$	1.03157	−	6.51305i	0.0513859	−	0.324438i
$404$		0			0
$405$	−0.0262368	+	20.1246i	−0.00130372	+	0.999999i
$406$		0			0
$407$	33.8451	−	33.8451i	1.67764	−	1.67764i
$408$		0			0
$409$	15.7176	+	5.10695i	0.777184	+	0.252522i	0.670637	−	0.741785i	$-0.266021\pi$
$409$	15.7176	+	5.10695i	0.777184	+	0.252522i	0.106547	+	0.994308i	$0.466021\pi$
$410$		0			0
$411$	6.43980	+	13.9996i	0.317652	+	0.690547i
$412$		0			0
$413$	−21.6009	+	11.0062i	−1.06291	+	0.541580i
$414$		0			0
$415$	−26.2540	+	8.58901i	−1.28876	+	0.421618i
$416$		0			0
$417$	−6.19343	+	1.74118i	−0.303293	+	0.0852659i
$418$		0			0
$419$	−0.401580	−	0.291765i	−0.0196184	−	0.0142536i	0.577933	−	0.816084i	$-0.303860\pi$
$419$	−0.401580	−	0.291765i	−0.0196184	−	0.0142536i	−0.597551	+	0.801831i	$0.703860\pi$
$420$		0			0
$421$	−5.08407	+	3.69379i	−0.247782	+	0.180025i	−0.704743	−	0.709462i	$-0.748938\pi$
$421$	−5.08407	+	3.69379i	−0.247782	+	0.180025i	0.456961	+	0.889487i	$0.348938\pi$
$422$		0			0
$423$	−2.37931	+	9.83858i	−0.115686	+	0.478368i
$424$		0			0
$425$	19.1680	−	9.86416i	0.929786	−	0.478482i
$426$		0			0
$427$	5.75847	−	11.3016i	0.278672	−	0.546924i
$428$		0			0
$429$	−14.3938	−	15.5971i	−0.694938	−	0.753033i
$430$		0			0
$431$	−7.36561	+	10.1379i	−0.354789	+	0.488325i	−0.948688	−	0.316215i	$-0.897588\pi$
$431$	−7.36561	+	10.1379i	−0.354789	+	0.488325i	0.593899	+	0.804540i	$0.297588\pi$
$432$		0			0
$433$	−26.6433	+	4.21988i	−1.28039	+	0.202795i	−0.759320	−	0.650717i	$-0.774468\pi$
$433$	−26.6433	+	4.21988i	−1.28039	+	0.202795i	−0.521074	+	0.853512i	$0.674468\pi$
$434$		0			0
$435$	−1.33130	−	1.43677i	−0.0638309	−	0.0688877i
$436$		0			0
$437$	12.0001	+	23.5516i	0.574045	+	1.12663i
$438$		0			0
$439$	−10.8500	+	3.52537i	−0.517841	+	0.168257i	−0.556265	−	0.831005i	$-0.687766\pi$
$439$	−10.8500	+	3.52537i	−0.517841	+	0.168257i	0.0384243	+	0.999262i	$0.487766\pi$
$440$		0			0
$441$	0.341246	−	4.24582i	0.0162498	−	0.202182i
$442$		0			0
$443$	−15.4331	−	15.4331i	−0.733251	−	0.733251i	0.238011	−	0.971262i	$-0.423504\pi$
$443$	−15.4331	−	15.4331i	−0.733251	−	0.733251i	−0.971262	+	0.238011i	$0.923504\pi$
$444$		0			0
$445$	−9.23097	+	4.72688i	−0.437590	+	0.224076i
$446$		0			0
$447$	28.6062	+	1.14772i	1.35303	+	0.0542853i
$448$		0			0
$449$	−34.8771			−1.64595			−0.822975	−	0.568077i	$-0.807688\pi$
$449$	−34.8771			−1.64595			−0.822975	+	0.568077i	$0.807688\pi$
$450$		0			0
$451$	−26.1558			−1.23163
$452$		0			0
$453$	9.12719	+	0.366196i	0.428833	+	0.0172054i
$454$		0			0
$455$	−11.5190	−	1.80064i	−0.540021	−	0.0844152i
$456$		0			0
$457$	23.6405	+	23.6405i	1.10585	+	1.10585i	0.993690	+	0.112165i	$0.0357786\pi$
$457$	23.6405	+	23.6405i	1.10585	+	1.10585i	0.112165	+	0.993690i	$0.464221\pi$
$458$		0			0
$459$	22.3878	−	0.823793i	1.04497	−	0.0384514i
$460$		0			0
$461$	−11.6988	+	3.80117i	−0.544868	+	0.177038i	−0.568501	−	0.822682i	$-0.692477\pi$
$461$	−11.6988	+	3.80117i	−0.544868	+	0.177038i	0.0236333	+	0.999721i	$0.492477\pi$
$462$		0			0
$463$	8.22226	+	16.1371i	0.382121	+	0.749955i	0.999321	−	0.0368518i	$-0.0117330\pi$
$463$	8.22226	+	16.1371i	0.382121	+	0.749955i	−0.617200	+	0.786806i	$0.711733\pi$
$464$		0			0
$465$	5.64171	−	10.1021i	0.261628	−	0.468473i
$466$		0			0
$467$	−16.3946	+	2.59664i	−0.758650	+	0.120158i	−0.523763	−	0.851864i	$-0.675472\pi$
$467$	−16.3946	+	2.59664i	−0.758650	+	0.120158i	−0.234887	+	0.972023i	$0.575472\pi$
$468$		0			0
$469$	6.27688	−	8.63938i	0.289839	−	0.398930i
$470$		0			0
$471$	−12.9421	−	14.0240i	−0.596339	−	0.646191i
$472$		0			0
$473$	−20.9843	+	41.1841i	−0.964860	+	1.89365i
$474$		0			0
$475$	11.9160	−	37.1833i	0.546744	−	1.70609i
$476$		0			0
$477$	15.3841	+	3.72042i	0.704391	+	0.170346i
$478$		0			0
$479$	−21.0507	+	15.2942i	−0.961831	+	0.698811i	−0.953575	−	0.301155i	$-0.902628\pi$
$479$	−21.0507	+	15.2942i	−0.961831	+	0.698811i	−0.00825583	+	0.999966i	$0.502628\pi$
$480$		0			0
$481$	15.3960	+	11.1858i	0.701996	+	0.510030i
$482$		0			0
$483$	13.3321	−	3.74811i	0.606633	−	0.170545i
$484$		0			0
$485$	−0.0730088	−	36.2099i	−0.00331516	−	1.64421i
$486$		0			0
$487$	12.2935	−	6.26384i	0.557071	−	0.283842i	−0.152702	−	0.988272i	$-0.548797\pi$
$487$	12.2935	−	6.26384i	0.557071	−	0.283842i	0.709773	+	0.704430i	$0.248797\pi$
$488$		0			0
$489$	11.2052	+	24.3591i	0.506716	+	1.10156i
$490$		0			0
$491$	21.5354	+	6.99728i	0.971879	+	0.315783i	0.751574	−	0.659648i	$-0.229295\pi$
$491$	21.5354	+	6.99728i	0.971879	+	0.315783i	0.220305	+	0.975431i	$0.429295\pi$
$492$		0			0
$493$	−1.54184	+	1.54184i	−0.0694409	+	0.0694409i
$494$		0			0
$495$	−14.2637	−	34.4009i	−0.641104	−	1.54620i
$496$		0			0
$497$	−3.80280	+	24.0099i	−0.170579	+	1.07699i
$498$		0			0
$499$			7.12077i			0.318770i	0.987217	+	0.159385i	$0.0509511\pi$
$499$			7.12077i			0.318770i	−0.987217	+	0.159385i	$0.949049\pi$
$500$		0			0
$501$	17.2837	−	2.03111i	0.772178	−	0.0907434i
$502$		0			0
$503$	20.1311	+	3.18846i	0.897602	+	0.142166i	0.588153	−	0.808750i	$-0.299855\pi$
$503$	20.1311	+	3.18846i	0.897602	+	0.142166i	0.309449	+	0.950916i	$0.399855\pi$
$504$		0			0
$505$	−10.3158	+	1.65520i	−0.459049	+	0.0736553i
$506$		0			0
$507$	−8.72492	+	11.0486i	−0.387487	+	0.490687i
$508$		0			0
$509$	−0.874684	+	2.69200i	−0.0387697	+	0.119321i	−0.968568	−	0.248748i	$-0.919981\pi$
$509$	−0.874684	+	2.69200i	−0.0387697	+	0.119321i	0.929799	+	0.368069i	$0.119981\pi$
$510$		0			0
$511$	1.58173	+	4.86808i	0.0699718	+	0.215351i
$512$		0			0
$513$	27.6183	−	29.7285i	1.21938	−	1.31254i
$514$		0			0
$515$	−15.2977	+	0.0308443i	−0.674098	+	0.00135916i
$516$		0			0
$517$	−2.93020	−	18.5006i	−0.128870	−	0.813654i
$518$		0			0
$519$	12.4215	−	22.1371i	0.545245	−	0.971711i
$520$		0			0
$521$	21.4218	+	29.4846i	0.938507	+	1.29174i	0.956447	+	0.291905i	$0.0942892\pi$
$521$	21.4218	+	29.4846i	0.938507	+	1.29174i	−0.0179402	+	0.999839i	$0.505711\pi$
$522$		0			0
$523$	−12.8556	−	6.55024i	−0.562135	−	0.286422i	0.149743	−	0.988725i	$-0.452155\pi$
$523$	−12.8556	−	6.55024i	−0.562135	−	0.286422i	−0.711878	+	0.702303i	$0.752155\pi$
$524$		0			0
$525$	−17.8811	−	9.93879i	−0.780394	−	0.433764i
$526$		0			0
$527$	−11.4767	−	5.84769i	−0.499934	−	0.254729i
$528$		0			0
$529$	6.78486	+	9.33856i	0.294994	+	0.406025i
$530$		0			0
$531$	11.8295	−	28.4253i	0.513354	−	1.23355i
$532$		0			0
$533$	−1.62682	−	10.2713i	−0.0704655	−	0.444901i
$534$		0			0
$535$	−7.27822	−	5.26555i	−0.314665	−	0.227650i
$536$		0			0
$537$	−21.9193	+	14.6197i	−0.945889	+	0.630888i
$538$		0			0
$539$	2.43575	+	7.49647i	0.104915	+	0.322896i
$540$		0			0
$541$	−9.28677	+	28.5817i	−0.399269	+	1.22882i	0.526317	+	0.850288i	$0.323572\pi$
$541$	−9.28677	+	28.5817i	−0.399269	+	1.22882i	−0.925586	+	0.378536i	$0.876428\pi$
$542$		0			0
$543$	−0.751213	−	0.593220i	−0.0322376	−	0.0254575i
$544$		0			0
$545$	3.91286	−	25.0314i	0.167609	−	1.07223i
$546$		0			0
$547$	−32.6302	−	5.16812i	−1.39517	−	0.220973i	−0.586839	−	0.809704i	$-0.699628\pi$
$547$	−32.6302	−	5.16812i	−1.39517	−	0.220973i	−0.808329	+	0.588731i	$0.799628\pi$
$548$		0			0
$549$	3.73447	+	15.6697i	0.159383	+	0.668769i
$550$		0			0
$551$			3.94945i			0.168252i
$552$		0			0
$553$	6.35668	−	40.1345i	0.270314	−	1.70669i
$554$		0			0
$555$	18.5846	+	27.7426i	0.788873	+	1.17761i
$556$		0			0
$557$	21.8255	−	21.8255i	0.924778	−	0.924778i	−0.0725847	−	0.997362i	$-0.523125\pi$
$557$	21.8255	−	21.8255i	0.924778	−	0.924778i	0.997362	+	0.0725847i	$0.0231247\pi$
$558$		0			0
$559$	−17.4781	−	5.67897i	−0.739243	−	0.240195i
$560$		0			0
$561$	−37.6631	+	17.3250i	−1.59014	+	0.731464i
$562$		0			0
$563$	−1.53782	+	0.783556i	−0.0648112	+	0.0330230i	−0.486096	−	0.873906i	$-0.661579\pi$
$563$	−1.53782	+	0.783556i	−0.0648112	+	0.0330230i	0.421285	+	0.906929i	$0.361579\pi$
$564$		0			0
$565$	5.70397	+	7.81765i	0.239968	+	0.328891i
$566$		0			0
$567$	−12.4392	−	17.2412i	−0.522398	−	0.724062i
$568$		0			0
$569$	10.8632	+	7.89256i	0.455408	+	0.330873i	0.791727	−	0.610875i	$-0.209182\pi$
$569$	10.8632	+	7.89256i	0.455408	+	0.330873i	−0.336319	+	0.941748i	$0.609182\pi$
$570$		0			0
$571$	13.8833	−	10.0868i	0.580999	−	0.422121i	−0.258085	−	0.966122i	$-0.583091\pi$
$571$	13.8833	−	10.0868i	0.580999	−	0.422121i	0.839084	+	0.544001i	$0.183091\pi$
$572$		0			0
$573$	35.1339	+	12.9947i	1.46774	+	0.542862i
$574$		0			0
$575$	−2.58007	+	16.7262i	−0.107596	+	0.697531i
$576$		0			0
$577$	−5.02409	+	9.86033i	−0.209156	+	0.410491i	−0.971623	−	0.236536i	$-0.923988\pi$
$577$	−5.02409	+	9.86033i	−0.209156	+	0.410491i	0.762467	+	0.647027i	$0.223988\pi$
$578$		0			0
$579$	6.68932	−	6.17326i	0.277999	−	0.256552i
$580$		0			0
$581$	17.1527	−	23.6086i	0.711613	−	0.979451i
$582$		0			0
$583$	−28.9285	+	4.58182i	−1.19810	+	0.189760i
$584$		0			0
$585$	12.6220	−	7.74095i	0.521855	−	0.320049i
$586$		0			0
$587$	−9.65285	−	18.9448i	−0.398416	−	0.781935i	0.601440	−	0.798918i	$-0.294594\pi$
$587$	−9.65285	−	18.9448i	−0.398416	−	0.781935i	−0.999856	+	0.0169832i	$0.994594\pi$
$588$		0			0
$589$	−22.1884	+	7.20945i	−0.914258	+	0.297060i
$590$		0			0
$591$	6.64550	−	33.2648i	0.273359	−	1.36833i
$592$		0			0
$593$	12.3241	+	12.3241i	0.506090	+	0.506090i	0.913324	−	0.407234i	$-0.133507\pi$
$593$	12.3241	+	12.3241i	0.506090	+	0.506090i	−0.407234	+	0.913324i	$0.633507\pi$
$594$		0			0
$595$	−10.2981	+	20.3122i	−0.422180	+	0.832720i
$596$		0			0
$597$	−0.122982	+	3.06525i	−0.00503332	+	0.125452i
$598$		0			0
$599$	−13.1359			−0.536716			−0.268358	−	0.963319i	$-0.586481\pi$
$599$	−13.1359			−0.536716			−0.268358	+	0.963319i	$0.586481\pi$
$600$		0			0
$601$	39.9534			1.62973			0.814867	−	0.579648i	$-0.196810\pi$
$601$	39.9534			1.62973			0.814867	+	0.579648i	$0.196810\pi$
$602$		0			0
$603$	1.04162	+	13.5219i	0.0424178	+	0.550655i
$604$		0			0
$605$	31.4003	+	31.2739i	1.27660	+	1.27147i
$606$		0			0
$607$	−8.63234	−	8.63234i	−0.350376	−	0.350376i	0.509874	−	0.860249i	$-0.329692\pi$
$607$	−8.63234	−	8.63234i	−0.350376	−	0.350376i	−0.860249	+	0.509874i	$0.829692\pi$
$608$		0			0
$609$	2.02916	+	0.405377i	0.0822258	+	0.0164267i
$610$		0			0
$611$	7.08288	−	2.30137i	0.286543	−	0.0931034i
$612$		0			0
$613$	12.3185	+	24.1765i	0.497541	+	0.976480i	0.994099	+	0.108476i	$0.0345971\pi$
$613$	12.3185	+	24.1765i	0.497541	+	0.976480i	−0.496558	+	0.868004i	$0.665403\pi$
$614$		0			0
$615$	3.53867	−	17.9011i	0.142693	−	0.721840i
$616$		0			0
$617$	16.2868	−	2.57957i	0.655681	−	0.103850i	0.180275	−	0.983616i	$-0.442301\pi$
$617$	16.2868	−	2.57957i	0.655681	−	0.103850i	0.475406	+	0.879766i	$0.342301\pi$
$618$		0			0
$619$	−7.86705	+	10.8281i	−0.316203	+	0.435216i	−0.937303	−	0.348515i	$-0.886686\pi$
$619$	−7.86705	+	10.8281i	−0.316203	+	0.435216i	0.621100	+	0.783731i	$0.286686\pi$
$620$		0			0
$621$	−9.80773	+	14.5995i	−0.393571	+	0.585857i
$622$		0			0
$623$	4.97392	−	9.76187i	0.199276	−	0.391101i
$624$		0			0
$625$	20.1063	−	14.8573i	0.804250	−	0.594291i
$626$		0			0
$627$	−26.0482	+	70.4266i	−1.04026	+	2.81257i
$628$		0			0
$629$	30.0732	−	21.8495i	1.19910	−	0.871196i
$630$		0			0
$631$	16.8778	+	12.2624i	0.671894	+	0.488160i	0.870659	−	0.491887i	$-0.163693\pi$
$631$	16.8778	+	12.2624i	0.671894	+	0.488160i	−0.198764	+	0.980047i	$0.563693\pi$
$632$		0			0
$633$	−1.50193	−	5.34242i	−0.0596964	−	0.212342i
$634$		0			0
$635$	−3.55970	−	1.14869i	−0.141262	−	0.0455842i
$636$		0			0
$637$	−2.79235	+	1.42277i	−0.110637	+	0.0563723i
$638$		0			0
$639$	−16.0870	−	26.3497i	−0.636392	−	1.04238i
$640$		0			0
$641$	19.5368	+	6.34790i	0.771658	+	0.250727i	0.668275	−	0.743915i	$-0.267033\pi$
$641$	19.5368	+	6.34790i	0.771658	+	0.250727i	0.103383	+	0.994642i	$0.467033\pi$
$642$		0			0
$643$	20.8324	−	20.8324i	0.821549	−	0.821549i	−0.164781	−	0.986330i	$-0.552692\pi$
$643$	20.8324	−	20.8324i	0.821549	−	0.821549i	0.986330	+	0.164781i	$0.0526917\pi$
$644$		0			0
$645$	−25.3474	−	19.9335i	−0.998051	−	0.784882i
$646$		0			0
$647$	6.10259	−	38.5303i	0.239918	−	1.51478i	−0.513988	−	0.857798i	$-0.671832\pi$
$647$	6.10259	−	38.5303i	0.239918	−	1.51478i	0.753905	−	0.656983i	$-0.228168\pi$
$648$		0			0
$649$			56.9743i			2.23644i
$650$		0			0
$651$	1.42665	+	12.1400i	0.0559149	+	0.475805i
$652$		0			0
$653$	−32.1247	−	5.08805i	−1.25714	−	0.199111i	−0.507901	−	0.861415i	$-0.669579\pi$
$653$	−32.1247	−	5.08805i	−1.25714	−	0.199111i	−0.749235	+	0.662304i	$0.769579\pi$
$654$		0			0
$655$	−9.16347	−	4.64577i	−0.358047	−	0.181525i
$656$		0			0
$657$	−5.53697	−	3.40571i	−0.216018	−	0.132870i
$658$		0			0
$659$	6.17031	−	18.9903i	0.240361	−	0.739755i	−0.756004	−	0.654567i	$-0.772851\pi$
$659$	6.17031	−	18.9903i	0.240361	−	0.739755i	0.996365	−	0.0851880i	$-0.0271491\pi$
$660$		0			0
$661$	−4.21748	−	12.9801i	−0.164041	−	0.504866i	0.834923	−	0.550366i	$-0.185512\pi$
$661$	−4.21748	−	12.9801i	−0.164041	−	0.504866i	−0.998964	+	0.0455001i	$0.985512\pi$
$662$		0			0
$663$	−9.14605	−	13.7127i	−0.355203	−	0.532555i
$664$		0			0
$665$	12.8257	+	39.2044i	0.497361	+	1.52028i
$666$		0			0
$667$	−0.267791	−	1.69077i	−0.0103689	−	0.0654668i
$668$		0			0
$669$	3.64551	+	2.04556i	0.140943	+	0.0790859i
$670$		0			0
$671$	−17.5213	−	24.1161i	−0.676404	−	0.930990i
$672$		0			0
$673$	−1.04272	−	0.531291i	−0.0401938	−	0.0204798i	0.433778	−	0.901020i	$-0.357180\pi$
$673$	−1.04272	−	0.531291i	−0.0401938	−	0.0204798i	−0.473972	+	0.880540i	$0.657180\pi$
$674$		0			0
$675$	25.4737	−	5.10790i	0.980483	−	0.196603i
$676$		0			0
$677$	−2.46293	−	1.25493i	−0.0946581	−	0.0482307i	0.406020	−	0.913864i	$-0.366916\pi$
$677$	−2.46293	−	1.25493i	−0.0946581	−	0.0482307i	−0.500679	+	0.865633i	$0.666916\pi$
$678$		0			0
$679$	22.4846	+	30.9474i	0.862881	+	1.18765i
$680$		0			0
$681$	−24.3927	−	13.6872i	−0.934730	−	0.524493i
$682$		0			0
$683$	−4.28310	−	27.0424i	−0.163888	−	1.03475i	−0.923283	−	0.384119i	$-0.874505\pi$
$683$	−4.28310	−	27.0424i	−0.163888	−	1.03475i	0.759395	−	0.650630i	$-0.225495\pi$
$684$		0			0
$685$	16.0708	−	11.7257i	0.614035	−	0.448017i
$686$		0			0
$687$	16.6330	+	24.9379i	0.634590	+	0.951440i
$688$		0			0
$689$	−3.59854	−	11.0752i	−0.137094	−	0.421931i
$690$		0			0
$691$	6.92199	−	21.3037i	0.263325	−	0.810430i	−0.728750	−	0.684780i	$-0.759898\pi$
$691$	6.92199	−	21.3037i	0.263325	−	0.810430i	0.992075	−	0.125650i	$-0.0401017\pi$
$692$		0			0
$693$	33.5104	+	20.6118i	1.27296	+	0.782977i
$694$		0			0
$695$	3.78560	+	7.39276i	0.143596	+	0.280424i
$696$		0			0
$697$	−20.0632	−	3.17770i	−0.759948	−	0.120364i
$698$		0			0
$699$	3.10513	+	26.4230i	0.117447	+	0.999410i
$700$		0			0
$701$			19.9094i			0.751969i	0.926626	+	0.375985i	$0.122695\pi$
$701$			19.9094i			0.751969i	−0.926626	+	0.375985i	$0.877305\pi$
$702$		0			0
$703$	10.5326	−	66.5005i	0.397246	−	2.50811i
$704$		0			0
$705$	13.0582	+	0.497545i	0.491801	+	0.0187386i
$706$		0			0
$707$	7.80455	−	7.80455i	0.293520	−	0.293520i
$708$		0			0
$709$	−16.9259	−	5.49956i	−0.635666	−	0.206540i	−0.0265827	−	0.999647i	$-0.508463\pi$
$709$	−16.9259	−	5.49956i	−0.635666	−	0.206540i	−0.609083	+	0.793106i	$0.708463\pi$
$710$		0			0
$711$	26.8907	+	44.0456i	1.00848	+	1.65184i
$712$		0			0
$713$	9.01008	−	4.59086i	0.337430	−	0.171929i
$714$		0			0
$715$	−16.0605	+	22.1993i	−0.600627	+	0.830208i
$716$		0			0
$717$	−9.37198	−	33.3364i	−0.350003	−	1.24497i
$718$		0			0
$719$	33.9545	+	24.6694i	1.26629	+	0.920014i	0.999048	−	0.0436153i	$-0.0138876\pi$
$719$	33.9545	+	24.6694i	1.26629	+	0.920014i	0.267242	+	0.963629i	$0.413888\pi$
$720$		0			0
$721$	13.0745	−	9.49915i	0.486918	−	0.353767i
$722$		0			0
$723$	−2.57937	+	6.97386i	−0.0959279	+	0.259361i
$724$		0			0
$725$	−1.47808	+	2.05175i	−0.0548946	+	0.0762002i
$726$		0			0
$727$	11.3404	−	22.2569i	0.420594	−	0.825462i	−0.579352	−	0.815077i	$-0.696694\pi$
$727$	11.3404	−	22.2569i	0.420594	−	0.825462i	0.999946	−	0.0103844i	$-0.00330552\pi$
$728$		0			0
$729$	26.2223	+	6.43369i	0.971195	+	0.238285i
$730$		0			0
$731$	−21.0998	+	29.0414i	−0.780405	+	1.07413i
$732$		0			0
$733$	30.1622	−	4.77723i	1.11407	−	0.176451i	0.427852	−	0.903849i	$-0.359270\pi$
$733$	30.1622	−	4.77723i	1.11407	−	0.176451i	0.686216	+	0.727398i	$0.259270\pi$
$734$		0			0
$735$	−5.46012	+	0.652817i	−0.201400	+	0.0240795i
$736$		0			0
$737$	−11.3936	−	22.3612i	−0.419688	−	0.823684i
$738$		0			0
$739$	18.0849	−	5.87616i	0.665266	−	0.216158i	0.0431325	−	0.999069i	$-0.486266\pi$
$739$	18.0849	−	5.87616i	0.665266	−	0.216158i	0.622133	+	0.782911i	$0.286266\pi$
$740$		0			0
$741$	−29.2765	−	5.84872i	−1.07550	−	0.214858i
$742$		0			0
$743$	−21.7526	−	21.7526i	−0.798025	−	0.798025i	0.184759	−	0.982784i	$-0.440850\pi$
$743$	−21.7526	−	21.7526i	−0.798025	−	0.798025i	−0.982784	+	0.184759i	$0.940850\pi$
$744$		0			0
$745$	−5.85543	−	36.4934i	−0.214526	−	1.33701i
$746$		0			0
$747$	2.84640	+	36.9510i	0.104144	+	1.35197i
$748$		0			0
$749$	9.49011			0.346761
$750$		0			0
$751$	−2.51184			−0.0916583			−0.0458292	−	0.998949i	$-0.514593\pi$
$751$	−2.51184			−0.0916583			−0.0458292	+	0.998949i	$0.514593\pi$
$752$		0			0
$753$	0.531003	−	13.2349i	0.0193508	−	0.482307i
$754$		0			0
$755$	−1.86826	−	11.6437i	−0.0679928	−	0.423758i
$756$		0			0
$757$	10.6543	+	10.6543i	0.387238	+	0.387238i	0.873701	−	0.486463i	$-0.161713\pi$
$757$	10.6543	+	10.6543i	0.387238	+	0.387238i	−0.486463	+	0.873701i	$0.661713\pi$
$758$		0			0
$759$	6.37602	−	31.9160i	0.231435	−	1.15848i
$760$		0			0
$761$	25.2259	−	8.19638i	0.914437	−	0.297119i	0.186254	−	0.982502i	$-0.440365\pi$
$761$	25.2259	−	8.19638i	0.914437	−	0.297119i	0.728183	+	0.685383i	$0.240365\pi$
$762$		0			0
$763$	12.1510	+	23.8477i	0.439896	+	0.863344i
$764$		0			0
$765$	−6.76175	−	28.1206i	−0.244471	−	1.01670i
$766$		0			0
$767$	−22.3737	+	3.54365i	−0.807867	+	0.127954i
$768$		0			0
$769$	12.4291	−	17.1072i	0.448206	−	0.616903i	−0.523805	−	0.851838i	$-0.675488\pi$
$769$	12.4291	−	17.1072i	0.448206	−	0.616903i	0.972011	+	0.234935i	$0.0754878\pi$
$770$		0			0
$771$	11.2286	−	10.3623i	0.404387	−	0.373190i
$772$		0			0
$773$	16.4953	−	32.3738i	0.593294	−	1.16441i	−0.377840	−	0.925871i	$-0.623333\pi$
$773$	16.4953	−	32.3738i	0.593294	−	1.16441i	0.971134	−	0.238534i	$-0.0766669\pi$
$774$		0			0
$775$	−14.2251	−	4.55868i	−0.510981	−	0.163753i
$776$		0			0
$777$	−33.0858	−	12.2372i	−1.18695	−	0.439007i
$778$		0			0
$779$	−29.7660	+	21.6263i	−1.06648	+	0.774842i
$780$		0			0
$781$	46.2186	+	33.5798i	1.65383	+	1.20158i
$782$		0			0
$783$	−2.29604	+	1.27835i	−0.0820539	+	0.0456843i
$784$		0			0
$785$	−14.4406	+	19.9604i	−0.515409	+	0.712416i
$786$		0			0
$787$	−25.7846	+	13.1379i	−0.919122	+	0.468316i	−0.848505	−	0.529188i	$-0.822497\pi$
$787$	−25.7846	+	13.1379i	−0.919122	+	0.468316i	−0.0706170	+	0.997504i	$0.522497\pi$
$788$		0			0
$789$	−27.3254	+	12.5697i	−0.972809	+	0.447493i
$790$		0			0
$791$	−9.72301	−	3.15920i	−0.345710	−	0.112328i
$792$		0			0
$793$	8.38054	−	8.38054i	0.297602	−	0.297602i
$794$		0			0
$795$	0.777988	−	20.4185i	0.0275924	−	0.724171i
$796$		0			0
$797$	1.30431	−	8.23509i	0.0462010	−	0.291702i	−0.953760	−	0.300570i	$-0.902823\pi$
$797$	1.30431	−	8.23509i	0.0462010	−	0.291702i	0.999961	+	0.00886857i	$0.00282299\pi$
$798$		0			0
$799$		−	14.5471i		−	0.514640i
$800$		0			0
$801$	3.22568	+	13.5349i	0.113974	+	0.478231i
$802$		0			0
$803$	11.8812	+	1.88179i	0.419278	+	0.0664070i
$804$		0			0
$805$	−8.14898	−	15.9139i	−0.287214	−	0.560890i
$806$		0			0
$807$	−28.9030	−	22.8242i	−1.01744	−	0.803451i
$808$		0			0
$809$	−10.7932	+	33.2182i	−0.379470	+	1.16789i	0.560943	+	0.827854i	$0.310439\pi$
$809$	−10.7932	+	33.2182i	−0.379470	+	1.16789i	−0.940413	+	0.340034i	$0.889561\pi$
$810$		0			0
$811$	−0.408186	−	1.25627i	−0.0143333	−	0.0441135i	0.943634	−	0.330991i	$-0.107383\pi$
$811$	−0.408186	−	1.25627i	−0.0143333	−	0.0441135i	−0.957967	+	0.286877i	$0.907383\pi$
$812$		0			0
$813$	13.8880	−	9.26300i	0.487073	−	0.324867i
$814$		0			0
$815$	27.9631	−	20.4026i	0.979504	−	0.714673i
$816$		0			0
$817$	10.1713	+	64.2188i	0.355848	+	2.24673i
$818$		0			0
$819$	−6.00995	+	14.4415i	−0.210005	+	0.504626i
$820$		0			0
$821$	7.54308	+	10.3822i	0.263255	+	0.362340i	0.920098	−	0.391688i	$-0.128109\pi$
$821$	7.54308	+	10.3822i	0.263255	+	0.362340i	−0.656843	+	0.754027i	$0.728109\pi$
$822$		0			0
$823$	33.4192	+	17.0279i	1.16492	+	0.593556i	0.926015	−	0.377487i	$-0.123212\pi$
$823$	33.4192	+	17.0279i	1.16492	+	0.593556i	0.238905	+	0.971043i	$0.423212\pi$
$824$		0			0
$825$	−39.8893	+	26.8383i	−1.38877	+	0.934391i
$826$		0			0
$827$	−14.4342	−	7.35461i	−0.501928	−	0.255745i	0.184646	−	0.982805i	$-0.440886\pi$
$827$	−14.4342	−	7.35461i	−0.501928	−	0.255745i	−0.686574	+	0.727060i	$0.740886\pi$
$828$		0			0
$829$	8.37217	+	11.5233i	0.290777	+	0.400221i	0.929266	−	0.369410i	$-0.120440\pi$
$829$	8.37217	+	11.5233i	0.290777	+	0.400221i	−0.638489	+	0.769631i	$0.720440\pi$
$830$		0			0
$831$	−27.2997	+	48.6524i	−0.947017	+	1.68773i
$832$		0			0
$833$	0.957623	+	6.04619i	0.0331797	+	0.209488i
$834$		0			0
$835$	−6.98565	−	21.3530i	−0.241748	−	0.738952i
$836$		0			0
$837$	−11.3731	−	10.5659i	−0.393113	−	0.365210i
$838$		0			0
$839$	12.4231	+	38.2343i	0.428892	+	1.32000i	0.899217	+	0.437502i	$0.144137\pi$
$839$	12.4231	+	38.2343i	0.428892	+	1.32000i	−0.470325	+	0.882493i	$0.655863\pi$
$840$		0			0
$841$	−8.88245	+	27.3374i	−0.306291	+	0.942668i
$842$		0			0
$843$	2.96379	−	3.75313i	0.102078	−	0.129265i
$844$		0			0
$845$	16.2106	+	8.21857i	0.557661	+	0.282727i
$846$		0			0
$847$	−46.2416	−	7.32395i	−1.58888	−	0.251654i
$848$		0			0
$849$	26.2152	−	3.08071i	0.899703	−	0.105730i
$850$		0			0
$851$			29.1832i			1.00039i
$852$		0			0
$853$	−4.09833	+	25.8759i	−0.140324	+	0.885973i	0.812613	+	0.582804i	$0.198045\pi$
$853$	−4.09833	+	25.8759i	−0.140324	+	0.885973i	−0.952937	+	0.303169i	$0.901955\pi$
$854$		0			0
$855$	−44.6759	−	27.3555i	−1.52788	−	0.935539i
$856$		0			0
$857$	−33.2839	+	33.2839i	−1.13696	+	1.13696i	−0.147964	+	0.988993i	$0.547272\pi$
$857$	−33.2839	+	33.2839i	−1.13696	+	1.13696i	−0.988993	+	0.147964i	$0.952728\pi$
$858$		0			0
$859$	30.3820	+	9.87171i	1.03662	+	0.336818i	0.777405	−	0.629001i	$-0.216536\pi$
$859$	30.3820	+	9.87171i	1.03662	+	0.336818i	0.259216	+	0.965819i	$0.416536\pi$
$860$		0			0
$861$	8.05600	+	17.5130i	0.274548	+	0.596843i
$862$		0			0
$863$	−28.4236	+	14.4825i	−0.967549	+	0.492991i	−0.865019	−	0.501739i	$-0.832694\pi$
$863$	−28.4236	+	14.4825i	−0.967549	+	0.492991i	−0.102530	+	0.994730i	$0.532694\pi$
$864$		0			0
$865$	−31.1870	−	10.0638i	−1.06039	−	0.342180i
$866$		0			0
$867$	−2.64885	+	0.744679i	−0.0899595	+	0.0252906i
$868$		0			0
$869$	−77.2581	−	56.1313i	−2.62080	−	1.90412i
$870$		0			0
$871$	8.07253	−	5.86504i	0.273527	−	0.198729i
$872$		0			0
$873$	−47.2196	−	11.4194i	−1.59814	−	0.386487i
$874$		0			0
$875$	−8.00925	+	25.1669i	−0.270762	+	0.850796i
$876$		0			0
$877$	11.9289	−	23.4117i	0.402809	−	0.790558i	−0.597124	−	0.802149i	$-0.703690\pi$
$877$	11.9289	−	23.4117i	0.402809	−	0.790558i	0.999933	+	0.0115917i	$0.00368982\pi$
$878$		0			0
$879$	−12.4154	−	13.4533i	−0.418760	−	0.453767i
$880$		0			0
$881$	5.23004	−	7.19854i	0.176205	−	0.242525i	−0.711775	−	0.702407i	$-0.752108\pi$
$881$	5.23004	−	7.19854i	0.176205	−	0.242525i	0.887980	+	0.459883i	$0.152108\pi$
$882$		0			0
$883$	45.7465	−	7.24553i	1.53949	−	0.243831i	0.671724	−	0.740802i	$-0.265554\pi$
$883$	45.7465	−	7.24553i	1.53949	−	0.243831i	0.867768	+	0.496970i	$0.165554\pi$
$884$		0			0
$885$	−38.9932	−	7.70816i	−1.31074	−	0.259107i
$886$		0			0
$887$	1.61971	+	3.17886i	0.0543846	+	0.106736i	0.916599	−	0.399808i	$-0.130923\pi$
$887$	1.61971	+	3.17886i	0.0543846	+	0.106736i	−0.862215	+	0.506543i	$0.830923\pi$
$888$		0			0
$889$	3.75810	−	1.22108i	0.126042	−	0.0409537i
$890$		0			0
$891$	−49.3742	+	7.65216i	−1.65410	+	0.256357i
$892$		0			0
$893$	−18.6314	−	18.6314i	−0.623475	−	0.623475i
$894$		0			0
$895$	24.1004	+	24.0034i	0.805586	+	0.802344i
$896$		0			0
$897$	12.9299	+	0.518766i	0.431717	+	0.0173211i
$898$		0			0
$899$	1.51093			0.0503924
$900$		0			0
$901$	−22.7466			−0.757800
$902$		0			0
$903$	34.0386	+	1.36568i	1.13273	+	0.0454468i
$904$		0			0
$905$	−0.558793	+	1.10218i	−0.0185749	+	0.0366377i
$906$		0			0
$907$	−8.84343	−	8.84343i	−0.293641	−	0.293641i	0.544876	−	0.838517i	$-0.316577\pi$
$907$	−8.84343	−	8.84343i	−0.293641	−	0.293641i	−0.838517	+	0.544876i	$0.816577\pi$
$908$		0			0
$909$	−1.12297	+	13.9721i	−0.0372466	+	0.463426i
$910$		0			0
$911$	30.2562	−	9.83082i	1.00243	−	0.325710i	0.238595	−	0.971119i	$-0.423313\pi$
$911$	30.2562	−	9.83082i	1.00243	−	0.325710i	0.763837	+	0.645410i	$0.223313\pi$
$912$		0			0
$913$	−31.1350	−	61.1058i	−1.03042	−	2.02231i
$914$		0			0
$915$	18.8755	−	8.72890i	0.624005	−	0.288568i
$916$		0			0
$917$	10.7199	−	1.69787i	0.354004	−	0.0560687i
$918$		0			0
$919$	−12.0511	+	16.5869i	−0.397529	+	0.547152i	−0.960122	−	0.279582i	$-0.909804\pi$
$919$	−12.0511	+	16.5869i	−0.397529	+	0.547152i	0.562593	+	0.826734i	$0.309804\pi$
$920$		0			0
$921$	−6.05400	−	6.56009i	−0.199486	−	0.216162i
$922$		0			0
$923$	−10.3120	+	20.2385i	−0.339425	+	0.666159i
$924$		0			0
$925$	30.3596	−	30.6054i	0.998217	−	1.00630i
$926$		0			0
$927$	−4.82438	+	19.9490i	−0.158453	+	0.655212i
$928$		0			0
$929$	−35.8841	+	26.0713i	−1.17732	+	0.855373i	−0.991867	−	0.127281i	$-0.959375\pi$
$929$	−35.8841	+	26.0713i	−1.17732	+	0.855373i	−0.185453	+	0.982653i	$0.559375\pi$
$930$		0			0
$931$	8.97020	+	6.51723i	0.293987	+	0.213594i
$932$		0			0
$933$	−13.9863	+	3.93202i	−0.457891	+	0.128729i
$934$		0			0
$935$	31.5458	+	43.2355i	1.03166	+	1.41395i
$936$		0			0
$937$	−1.10010	+	0.560530i	−0.0359388	+	0.0183117i	−0.471868	−	0.881669i	$-0.656420\pi$
$937$	−1.10010	+	0.560530i	−0.0359388	+	0.0183117i	0.435929	+	0.899981i	$0.356420\pi$
$938$		0			0
$939$	−6.42502	−	13.9674i	−0.209673	−	0.455810i
$940$		0			0
$941$	33.2056	+	10.7891i	1.08247	+	0.351716i	0.795333	−	0.606173i	$-0.207296\pi$
$941$	33.2056	+	10.7891i	1.08247	+	0.351716i	0.287138	+	0.957889i	$0.407296\pi$
$942$		0			0
$943$	11.2765	−	11.2765i	0.367214	−	0.367214i
$944$		0			0
$945$	−18.6404	+	20.1459i	−0.606372	+	0.655346i
$946$		0			0
$947$	6.31969	−	39.9009i	0.205362	−	1.29661i	−0.642457	−	0.766321i	$-0.722085\pi$
$947$	6.31969	−	39.9009i	0.205362	−	1.29661i	0.847820	−	0.530285i	$-0.177915\pi$
$948$		0			0
$949$			4.78275i			0.155255i
$950$		0			0
$951$	25.5584	−	3.00353i	0.828789	−	0.0973962i
$952$		0			0
$953$	−51.8286	−	8.20885i	−1.67889	−	0.265911i	−0.757017	−	0.653395i	$-0.773344\pi$
$953$	−51.8286	−	8.20885i	−1.67889	−	0.265911i	−0.921876	+	0.387484i	$0.873344\pi$
$954$		0			0
$955$	7.46895	−	47.7804i	0.241689	−	1.54614i
$956$		0			0
$957$	3.01381	−	3.81649i	0.0974228	−	0.123369i
$958$		0			0
$959$	−6.49440	+	19.9877i	−0.209715	+	0.645437i
$960$		0			0
$961$	−6.82142	−	20.9942i	−0.220046	−	0.677232i
$962$		0			0
$963$	−9.17760	+	7.81210i	−0.295744	+	0.251741i
$964$		0			0
$965$	−9.52092	−	6.88807i	−0.306489	−	0.221735i
$966$		0			0
$967$	2.62324	+	16.5625i	0.0843578	+	0.532614i	0.993288	+	0.115666i	$0.0369003\pi$
$967$	2.62324	+	16.5625i	0.0843578	+	0.532614i	−0.908930	+	0.416948i	$0.863100\pi$
$968$		0			0
$969$	−28.5368	+	50.8571i	−0.916734	+	1.63376i
$970$		0			0
$971$	−29.3538	−	40.4020i	−0.942008	−	1.29656i	−0.954987	−	0.296647i	$-0.904131\pi$
$971$	−29.3538	−	40.4020i	−0.942008	−	1.29656i	0.0129790	−	0.999916i	$-0.495869\pi$
$972$		0			0
$973$	−7.81794	−	3.98344i	−0.250632	−	0.127703i
$974$		0			0
$975$	−13.0204	−	13.9952i	−0.416985	−	0.448204i
$976$		0			0
$977$	54.4219	+	27.7294i	1.74111	+	0.887141i	0.967265	+	0.253768i	$0.0816699\pi$
$977$	54.4219	+	27.7294i	1.74111	+	0.887141i	0.773847	+	0.633373i	$0.218330\pi$
$978$		0			0
$979$	−15.1342	−	20.8304i	−0.483691	−	0.665743i
$980$		0			0
$981$	−31.3819	−	13.0599i	−1.00195	−	0.416970i
$982$		0			0
$983$	1.42079	+	8.97053i	0.0453163	+	0.286116i	0.999931	−	0.0117271i	$-0.00373293\pi$
$983$	1.42079	+	8.97053i	0.0453163	+	0.286116i	−0.954615	+	0.297843i	$0.903733\pi$
$984$		0			0
$985$	−43.7932	+	0.0882988i	−1.39537	+	0.00281343i
$986$		0			0
$987$	−11.4848	+	7.66014i	−0.365566	+	0.243825i
$988$		0			0
$989$	−8.70868	−	26.8026i	−0.276920	−	0.852272i
$990$		0			0
$991$	4.23922	−	13.0470i	0.134663	−	0.414451i	−0.860874	−	0.508818i	$-0.830083\pi$
$991$	4.23922	−	13.0470i	0.134663	−	0.414451i	0.995537	+	0.0943669i	$0.0300827\pi$
$992$		0			0
$993$	16.1162	+	12.7267i	0.511433	+	0.403870i
$994$		0			0
$995$	3.91039	−	0.627429i	0.123968	−	0.0198908i
$996$		0			0
$997$	19.1620	+	3.03495i	0.606865	+	0.0961180i	0.452302	−	0.891865i	$-0.350603\pi$
$997$	19.1620	+	3.03495i	0.606865	+	0.0961180i	0.154563	+	0.987983i	$0.450603\pi$
$998$		0			0
$999$	42.0697	−	15.4014i	1.33103	−	0.487280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.x.a.17.1	✓	80
3.2	odd	2	inner	300.2.x.a.17.10	yes	80
25.3	odd	20	inner	300.2.x.a.53.10	yes	80
75.53	even	20	inner	300.2.x.a.53.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.17.1	✓	80	1.1	even	1	trivial
300.2.x.a.17.10	yes	80	3.2	odd	2	inner
300.2.x.a.53.1	yes	80	75.53	even	20	inner
300.2.x.a.53.10	yes	80	25.3	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73066 - 0.0694365i) q^{3} +(0.354250 + 2.20783i) q^{5} +(-1.67035 - 1.67035i) q^{7} +(2.99036 + 0.240342i) q^{9} +O(q^{10})\)	\(q+(-1.73066 - 0.0694365i) q^{3} +(0.354250 + 2.20783i) q^{5} +(-1.67035 - 1.67035i) q^{7} +(2.99036 + 0.240342i) q^{9} +(-5.27981 + 1.71551i) q^{11} +(-1.00207 - 1.96667i) q^{13} +(-0.459783 - 3.84559i) q^{15} +(-4.25837 + 0.674459i) q^{17} +(-4.59013 + 6.31777i) q^{19} +(2.77483 + 3.00680i) q^{21} +(1.53667 - 3.01588i) q^{23} +(-4.74901 + 1.56425i) q^{25} +(-5.15860 - 0.623589i) q^{27} +(0.409155 - 0.297269i) q^{29} +(2.41697 + 1.75603i) q^{31} +(9.25666 - 2.60236i) q^{33} +(3.09613 - 4.27958i) q^{35} +(-7.68210 + 3.91423i) q^{37} +(1.59768 + 3.47321i) q^{39} +(4.48088 + 1.45593i) q^{41} +(5.88737 - 5.88737i) q^{43} +(0.528702 + 6.68734i) q^{45} +(-0.527820 + 3.33252i) q^{47} -1.41984i q^{49} +(7.41661 - 0.871573i) q^{51} +(5.21091 + 0.825328i) q^{53} +(-5.65793 - 11.0492i) q^{55} +(8.38263 - 10.6152i) q^{57} +(3.17139 - 9.76054i) q^{59} +(1.65928 + 5.10673i) q^{61} +(-4.59350 - 5.39641i) q^{63} +(3.98709 - 2.90909i) q^{65} +(0.707187 + 4.46500i) q^{67} +(-2.86886 + 5.11276i) q^{69} +(-6.04875 - 8.32540i) q^{71} +(-1.93067 - 0.983727i) q^{73} +(8.32754 - 2.37742i) q^{75} +(11.6847 + 5.95363i) q^{77} +(10.1110 + 13.9166i) q^{79} +(8.88447 + 1.43741i) q^{81} +(1.93251 + 12.2014i) q^{83} +(-2.99762 - 9.16282i) q^{85} +(-0.728750 + 0.486061i) q^{87} +(1.43321 + 4.41098i) q^{89} +(-1.61123 + 4.95884i) q^{91} +(-4.06102 - 3.20692i) q^{93} +(-15.5746 - 7.89614i) q^{95} +(-15.9942 - 2.53324i) q^{97} +(-16.2008 + 3.86104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q - 2 * q^3 + 4 * q^7	\( 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) \) 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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